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Journal of Economic Perspectives—Volume 19, Number 4 —Fall 2005—Pages 67–92
Assessing High House Prices: Bubbles,
Fundamentals and Misperceptions
Charles Himmelberg, Christopher Mayer and
Todd Sinai
H
ouse price watching has become a national pastime. By 2004, 68 percent
of households owned their own homes and, for most of them, housing
equity will make up nearly all of their nonpension assets at retirement
(Venti and Wise, 1991). Many of the 32 percent who rent are younger households,
owners-in-waiting who watch housing markets with great interest (or concern). The
preoccupation with housing markets has been particularly strong of late because
recent house price growth has been rampant, especially in certain cities. Between
1975 and 1995, real single-family house prices in the United States increased an
average of 0.5 percent per year, or 10 percent over the course of two decades. By
contrast, from 1995 to 2004, national real house prices grew 3.6 percent per year,
a more than seven-fold increase in the annual rate of real appreciation, and totaling
nearly 40 percent in one decade. In some individual cities, such as San Francisco
and Boston, real home prices grew about 75 percent from 1995 to 2004, almost
double the national average.
How does one tell when rapid growth in house prices is caused by fundamental
factors of supply and demand and when it is an unsustainable bubble? Stiglitz
(1990) provided a general definition of asset bubbles in this journal: “[I]f the
reason that the price is high today is only because investors believe that the selling
price is high tomorrow—when ‘fundamental’ factors do not seem to justify such a
y Charles Himmelberg is Senior Economist, Federal Reserve Bank of New York, New York,
New York. Christopher Mayer is Paul Milstein Professor, Finance and Economics, Columbia
Business School, Columbia University, New York, New York. Todd Sinai is Associate Professor
of Real Estate, Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania.
Mayer is also Research Associate, and is a Sinai Faculty Research Fellow, National
Bureau of Economic Research, Cambridge, Massachusetts. Their e-mail addresses are
具[email protected]典, 具[email protected]典 and 具[email protected]典,
respectively.
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Journal of Economic Perspectives
price—then a bubble exists. At least in the short run, the high price of the asset is
merited, because it yields a return (capital gain plus dividend) equal to that on
alternative assets.” The “dividend” portion of the return from owning a house
comes from the rent the owner saves by living in the house rent-free and the capital
gain comes from house price appreciation over time. We think of a housing bubble
as being driven by homebuyers who are willing to pay inflated prices for houses
today because they expect unrealistically high housing appreciation in the future.1
In this paper, we explain how to assess the state of house prices— both whether
there is a bubble and what underlying factors support housing demand—in a way
that is grounded in economic theory. In doing so, we correct four common fallacies
about the costliness of the housing market. First, the price of a house is not the
same as the annual cost of owning, so it does not necessarily follow from rising
prices of houses that ownership is becoming more expensive. Second, high price
growth is not evidence per se that housing is overvalued. In some local housing
markets, house price growth can exceed the national average rate of appreciation
for very long periods of time. Third, differences in expected appreciation rates and
taxes can lead to considerable variability in the price-to-rent ratio across markets.
Finally, the sensitivity of house prices to changes in fundamentals is higher at times
when real, long-term interest rates are already low and in cities where expected
price growth is high, so accelerating house price growth and outsized price increases in certain markets are not intrinsically signs of a bubble. For all of the above
reasons, conventional metrics for assessing pricing in the housing market such as
price-to-rent ratios or price-to-income ratios generally fail to reflect accurately the
state of housing costs. To the eyes of analysts employing such measures, housing
markets can appear “exuberant” even when houses are in fact reasonably priced.
We construct a measure for evaluating the cost of home owning that is standard for
economists—the imputed annual rental cost of owning a home, a variant of the
user cost of housing—and apply it to 25 years of history across a wide variety of
housing markets. This calculation enables us to estimate the time pattern of
housing costs within a market. Given the relatively short time series, it is hard to say
just how costly a market must become before it is unsustainably expensive. However, we
can determine how expensive a market is currently relative to its own history.
As of the end of 2004, our analysis reveals little evidence of a housing bubble.
In high-appreciation markets like San Francisco, Boston and New York, current
housing prices are not cheap, but our calculations do not reveal large price
increases in excess of fundamentals. For such cities, expectations of outsized capital
gains appear to play, at best, a very small role in single-family house prices. Rather,
recent price growth is supported by basic economic factors such as low real
long-term interest rates, high income growth and housing price levels that had
fallen to unusually low levels during the mid-1990s. The growth in price-to-rent
ratios— especially in cities where this ratio was already high— can be explained by
the fact that house prices are more sensitive to real long-term interest rates when
1
Case and Shiller (2004) also use this definition.
Charles Himmelberg, Christopher Mayer and Todd Sinai
69
interest rates are already low and even more sensitive in cities where house price growth
is typically high. During the late 1980s, our metrics indicate that house prices in many
cities were, in fact, overvalued (for example, Boston, Los Angeles, New York and San
Francisco), and prices in these cities subsequently fell. Thus, we do not find that
housing prices are always close to equilibrium levels. Still, in 2004, prices looked
reasonable. Only a few cities, such as Miami, Fort Lauderdale, Portland (Oregon) and,
to a degree, San Diego, had valuation ratios approaching those of the 1980s.
Of course, just because the data do not indicate bubbles in most cities in 2004
does not mean that prices cannot fall. Deterioration in underlying economic
fundamentals, such as an unexpected future rise in real long-term interest rates or
a decline in economic growth, could easily cause a fall in house prices. Indeed,
because real long-term interest rates are currently so low, our calculations suggest
that housing costs are more sensitive to changes in real long-term interest rates now
than any other time in the last 25 years. Finally, our data do not cover and hence
do not allow us to comment on the condominium market, which due to its lower
transaction costs and higher liquidity may be more vulnerable to overvaluation and
overbuilding arising from investor speculation.
How Not to Judge the Sustainability of Housing Prices
To assess whether house prices are unsustainably high, casual observers often
begin by looking at house price growth. Figure 1 shows that between 1980 and
2004, real house prices at the national level grew 39 percent, or 1.4 percent
annually. To compute these numbers, we use data from the Office of Federal
Housing Enterprise Oversight (OFHEO), which produces the most widely quoted
single-family house price index. The OFHEO price index is based on multiple
observations of the price of a given house, so unlike a conventional price index, it
controls to some extent for the changing quality in the mix of houses sold at any
given time, although changes in quality due to home renovations will not be
normalized using this index. These housing price data are available for over
100 metropolitan areas since 1980. An index cannot be used to compare price
levels across cities, but it can be used to calculate growth rates and to compare
prices over time. The major drawbacks of these data are that they are subject to
biases due to changes in the quality of existing houses, and they cover only those
houses with so-called “conventional” mortgages that have been purchased by
Fannie Mae and Freddie Mac. Since the current maximum lending limit for such
mortgages in 2005 is $359,650 for states in the continental United States, highpriced houses are underrepresented in the OFHEO index.2
2
This is a potentially important caveat because markets for high-priced houses may behave differently.
Mayer (1993), for example, shows that the prices of high-priced houses are more volatile than the values
of lower-priced properties. The National Association of Realtors (NAR) produces an index that is not
subject to the cap, but which does not control for changes in the mix of houses that sell over time. Our
conclusions are unchanged if we use the NAR index for our analysis instead of the OFHEO index.
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Journal of Economic Perspectives
Figure 1
Real U.S. House Price Index, Price-to-Rent and Price-to-Income Ratios
(ratios normalized to their 25-year average)
1.4
1.2
Real price
Price/Rent
1
Price/Income
.8
1980
1985
1990
1995
2000
2005
Source: OFHEO Price Index, REIS Inc., BEA, BLS CPI Index-All Urban Consumers.
Over the last quarter century, run-ups in house prices are common, but so are
subsequent declines. The national average real house price fell by 7.2 percent from
1980 to 1982; rose by 16.2 percent from 1982 to 1989; fell by 8 percent from 1989
to 1995; and then rose by 40 percent from 1995 to 2004. About one-third of the
increase in real housing prices since 1995 reflects the return of house prices to their
previous real peak of 1989. Housing prices in 2004 have since risen to levels
29 percent over the previous 1989 peak. Of course, these summary descriptions and
graphs of prices do not reveal whether fundamental factors or a price bubble are
at work in the first half of the 2000s; we shall return to this question.
The national average masks considerable differences across metropolitan statistical areas. Table 1 presents index values that are standardized so that a value of
1.0 corresponds to the average price level in a metropolitan statistical area over the
1980 –2004 period. We include all 46 metropolitan areas with available data on
house price changes, rents and per capita income for the comparisons that follow.
Over that time period, metro area house prices have followed one of three patterns.
In about half of the cities, including Boston, New York and San Francisco, house
prices peaked in the late 1980s, fell to a trough in the 1990s and rebounded by
2004. Prices in 18 more metropolitan areas, including Miami and Denver, have a
“U”-shaped history: high in the early 1980s and high again by the end of the sample.
A few cities, such as Houston and New Orleans, follow a third pattern; real house
prices have declined since 1980 and have not fully recovered. The first three
columns of Table 1 report the value of the house price index at three points in
time: the most recent house price peak, the subsequent trough and as of 2004.
Of the cities in the first category, a few have exhibited extraordinary appreciation since their mid-1990s trough. For example, by 2004, single-family house prices
Table 1
Conventional Measures of House Price Dynamics
Real price index
At
prior
peak
At prior
trough
In
2004
Price-to-rent ratio
At
prior
peak
At prior
trough
In
2004
Price-to-income ratio
At
prior
peak
Markets where house prices peaked in the late 1980s and had a trough in the 1990s:
Atlanta, GA
1.04
0.91
1.20 1.04
0.89
1.15 1.22
Austin, TX
1.23
0.92
1.13 1.42
0.86
1.05 1.31
Baltimore, MD
1.08
0.96
1.41 1.03
0.97
1.25 1.11
Boston, MA
1.21
0.86
1.67 1.19
0.90
1.36 1.28
Dallas, TX
1.23
0.84
0.99 1.26
0.85
0.96 1.38
District of Columbia, DC
1.14
0.92
1.50 1.11
0.96
1.31 1.12
Jacksonville, FL
1.05
0.89
1.34 1.06
0.90
1.25 1.22
Los Angeles, CA
1.27
0.83
1.59 1.21
0.98
1.41 1.23
Nashville, TN
1.04
0.89
1.17 1.05
0.95
1.14 1.24
New York, NY
1.26
0.91
1.54 1.36
0.82
1.19 1.29
Norfolk, VA
1.08
0.94
1.30 1.09
0.97
1.16 1.16
Oakland, CA
1.11
0.85
1.68 1.14
0.87
1.51 1.17
Orange County, CA
1.20
0.82
1.68 1.18
0.90
1.49 1.18
Philadelphia, PA
1.18
0.95
1.36 1.14
0.97
1.25 1.19
Phoenix, AZ
1.09
0.84
1.25 1.04
0.91
1.25 1.23
Portland, OR
1.24
1.23
1.40 1.06
0.72
1.41 1.18
Raleigh-Durham, NC
1.05
0.93
1.11 1.11
0.96
1.08 1.26
Richmond, VA
1.04
0.96
1.22 1.04
0.95
1.15 1.23
Sacramento, CA
1.16
0.86
1.63 1.20
0.88
1.34 1.20
San Bernadino-Riverside, CA 1.19
0.80
1.55 1.13
0.90
1.37 1.16
San Diego, CA
1.11
0.84
1.83 1.12
0.90
1.52 1.14
San Francisco, CA
1.15
0.87
1.65 1.26
0.82
1.44 1.21
San Jose, CA
1.11
0.86
1.62 1.22
0.81
1.62 1.21
Seattle, WA
1.04
1.01
1.45 1.04
0.95
1.35 1.08
Markets where house prices were high in the early 1980s and rebounded in the 2000s:
Charlotte, NC
1.02
0.95
1.14 1.05
0.97
1.10 1.28
Chicago, IL
1.00
1.00
1.37 1.04
0.98
1.29 1.06
Cincinnati, OH
1.06
0.95
1.17 1.14
0.90
1.14 1.30
Cleveland, OH
1.04
0.86
1.18 1.09
0.87
1.20 1.23
Columbus, OH
0.99
0.95
1.18 1.03
0.95
1.19 1.24
Denver, CO
1.00
0.75
1.39 1.01
0.87
1.22 1.21
Detroit, MI
1.00
0.72
1.39 0.98
0.70
1.42 1.21
Fort Lauderdale, FL
1.05
0.88
1.51 1.11
0.86
1.43 1.25
Indianapolis, IN
1.03
0.97
1.10 1.03
1.03
1.17 1.27
Kansas City, KS
1.16
0.87
1.18 1.28
0.92
1.17 1.39
Memphis, TN
1.06
1.03
1.06 1.10
0.95
1.01 1.32
Miami, FL
1.05
0.94
1.58 0.99
0.98
1.45 1.24
Milwaukee, MN
1.07
0.85
1.32 1.10
0.82
1.36 1.25
Minneapolis, MN
1.02
0.87
1.48 1.00
0.97
1.45 1.27
Orlando, FL
1.05
0.89
1.26 1.13
0.88
1.18 1.23
Pittsburgh, PA
1.07
1.03
1.17 1.06
1.04
1.20 1.26
St. Louis, MO
1.08
0.92
1.22 1.01
0.99
1.23 1.33
Tampa, FL
1.04
0.88
1.38 1.04
0.90
1.28 1.22
Markets where house prices have declined since the early 1980s and never fully rebounded:
Fort Worth, TX
1.23
0.85
0.97 1.25
0.85
0.95 1.45
Houston, TX
1.38
0.82
1.02 1.30
0.84
0.96 1.50
New Orleans, LA
1.24
0.80
1.16 1.08
0.86
1.19 1.42
San Antonio, TX
1.30
0.83
0.97 1.40
0.83
0.95 1.47
At prior
trough
In
2004
0.87
0.78
0.86
0.85
0.77
0.85
0.84
0.84
0.92
0.85
0.88
0.84
0.83
0.86
0.89
1.04
0.88
0.90
0.83
0.84
0.84
0.87
0.87
0.99
1.07
0.94
1.17
1.36
0.88
1.27
1.16
1.48
0.95
1.34
1.14
1.38
1.56
1.14
1.12
1.25
0.98
1.08
1.47
1.52
1.55
1.37
1.32
1.23
0.89
0.94
0.92
0.97
0.92
0.93
0.91
0.84
0.88
0.87
0.86
0.91
0.95
0.86
0.84
0.88
0.88
0.83
0.97
1.23
0.98
1.06
1.00
1.17
1.19
1.40
0.93
1.02
0.86
1.46
1.13
1.25
1.13
0.98
1.05
1.22
0.75
0.76
0.89
0.72
0.86
0.87
0.96
0.81
Notes: Twenty-five-year within-MSA average is normalized to 1.00. Values are not comparable across
markets. 2004 figures are in bold when they exceed their prior peak values.
72
Journal of Economic Perspectives
in Boston and seven California cities had risen more than 85 percent (adjusted for
inflation), with San Diego prices going up almost 120 percent to a level 83 percent
above their 25-year average. Much of this increase merely offset prior house price
declines, which were as much as 34 percent in Los Angeles and 25 percent or more
in seven other cities (from peak to trough). But even relative to their prior peak
house prices, most of these cities (excluding the two in Texas) have appreciated
considerably. House prices in San Diego, Boston and New York, for example, were
up 83, 38 and 22 percent above their respective prior peaks.3
Real house prices in the middle group—for example, Austin, Cincinnati,
Cleveland, Memphis, Kansas City, Pittsburgh and St. Louis—all exceeded their
25-year average by 2004, with Miami and Fort Lauderdale more than 50 percent
above average. Real housing values in a few markets even declined, as in Dallas, Fort
Worth, Houston, New Orleans and San Antonio, with real annual house prices in
Houston falling 1.2 percent per year, on average.4
A second commonly cited measure used to assess housing valuations is the
house price-to-rent ratio, which is akin to a price-to-earnings multiple for stocks.
This metric is intended to reflect the relative cost of owning versus renting.
Intuitively, when house prices are too high relative to rents, potential homebuyers
will choose instead to rent, thus reducing the demand for houses and bringing
house prices back into line with rents. A common argument is that when price-torent ratios remain high for a prolonged period, it must be that prices are being
sustained by unrealistic expectations of future price gains rather than the fundamental rental value and hence contain a “bubble.”
We obtained data on metro area rents between 1980 and 2004 from REIS, a
real estate consulting firm. REIS provides annual average rents for a “representative” two-bedroom apartment in each metro area listed in Table 1. As with the
OFHEO house price indexes, the rent data attempt to hold the quality of the rental
unit constant over time. Again, we cannot compare rent levels across markets
because our rent indices are not standardized to the same representative apartment
across markets. We can, however, construct a metro area index of real house prices
relative to real rents and compare movements in this index over time. As before, we
standardize the price-to-rent index so that a value of 1.0 corresponds to the average
value over the 1980 –2004 period.
Figure 1 shows that the price-to-rent ratio roughly tracks the overall house
price movement. After 1989, the price-to-rent ratio slowly declined, reaching a
trough in 2000. In the succeeding four years, the price-to-rent ratio grew 27 percent, leaving the ratio 15 percent above its previous peak (in 1989). By way of
comparison, the prior trough-to-peak swing, from 1985 to 1989, was less than
one-half the growth in the price-to-rent ratio from 2000 –2004. The 1989 peak
3
House prices in these cities appear more volatile in booms and busts, a point emphasized by Case and
Shiller (2004). We discuss this point in more detail below.
4
In an on-line appendix appended to this article at the website 具http://www.e-jep.org典, Figure 1 plots
house price indexes for all 46 metropolitan statistical areas in our data.
Charles Himmelberg, Christopher Mayer and Todd Sinai
73
occurred right before a housing price decline, lending weight to the view that the
price-to-rent ratio is an indicator of overheating in the housing market.
At the metropolitan statistical area level, many of the markets with a high
growth rate of price-to-rent since their prior trough are the same markets that saw
large price appreciation (for example, cities in California and the northeast).5 San
Jose and Detroit experienced a doubling of their price-to-rent ratios since their
prior troughs, and Portland, Oregon, experienced 95 percent growth.
More striking is the fact that the price-to-rent ratio in 2004 exceeds the 25-year
average everywhere except for four cities in Texas and surpasses the prior peak in
80 percent of the cities. Column 6 (Table 1) shows the ratio of price-to-rent in 2004
relative to its average value from 1980 –2004. In three of those cities, the price-torent ratio in 2004 exceeds its average value by more than 50 percent. San Francisco
is 14 percent above its prior peak, and New York is 12 percent below.
A third measure that is commonly used to assess whether housing prices
are “too high” is the price-to-income ratio. Unlike the price-to-rent ratio, which
measures the relative cost of owning and renting, the price-to-income ratio provides
a measure of local housing costs relative to the local ability to pay.
Figure 1 shows the price-to-income ratio computed as the OFHEO price index
divided by an index of mean per capita income based on data from the U.S. Bureau
of Economic Analysis. At the national level, this ratio declined in the early 1980s,
partially recovered to peak in 1987 and then declined again over the next decade,
bottoming out 23 percent below its 1980 level. After 1998, the price-to-income ratio
began to rise again and by 2003 had exceeded its 1988 peak. Despite growing
21 percent over the last six years, it has not yet returned to its 1980 level. The
decline in this ratio during most of the 1990s reveals that the growth in real house
prices nationally was outpaced by the high growth in incomes (McCarthy and
Peach, 2004).
At the metro area level, as shown in the last three columns in Table 1,
price-to-income ratios have generally increased the most in cities where house price
growth has been highest. Price-to-income is above its peak value in many of these
cities (though not by nearly as much as the price-to-rent ratio) and as much as
40 –50 percent above its 25-year average (the last column of Table 1). Yet there is
a lot of heterogeneity in this measure of house price excess. In Houston, Dallas and
other southern cities, price-to-income is well below its 25-year average.
If high growth rates of house prices, price-to-rent ratios and price-to-income
ratios were reliable indicators of a rising cost of obtaining housing, then these
recent trends would indeed provide reasons to suspect overvaluation in many
housing markets. However, as this paper will explain, these measures are inadequate to assess whether the housing market is the grip of a speculative bubble.
5
A few other markets, such as Miami, Milwaukee, Minneapolis and Portland, saw their price-to-rent ratio
rise by more than 50 percent. These all are markets that experienced economic declines in the 1970s
and 1980s, but have recovered appreciably since then.
74
Journal of Economic Perspectives
The User Cost of Housing
The key mistake committed by the conventional measures of overheating in
housing markets is that they erroneously treat the purchase price of a house as if it
were the same as the annual cost of owning. But consider purchasing a house for
$1 million. The cost of living in that house for one year is not $1 million. Nor is the
financial return on the house equal to just the capital gain or loss on that property.
A correct calculation of the financial return associated with an owner-occupied
property compares the value of living in that property for a year—the “imputed
rent,” or what it would have cost to rent an equivalent property—with the lost
income that one would have received if the owner had invested the capital in an
alternative investment—the “opportunity cost of capital.” This comparison should
take into account differences in risk, tax benefits from owner-occupancy, property
taxes, maintenance expenses and any anticipated capital gains from owning the home.
This line of reasoning is the basis for an economically justified way of evaluating whether the level of housing prices is “too high” or “too low.” We calculate the
true one-year cost of owning a house (the “user cost”), which can then be compared
to rental costs or income levels to judge whether the cost of owning is out of line
with the cost of renting, or unaffordable at local income levels. This section reviews
the most commonly used procedure for calculating the annual cost of homeownership, discusses its implications for house prices and then reviews the assumptions
that enter the calculation. In this framework, a house price bubble occurs when
homeowners have unreasonably high expectations about future capital gains, leading them to perceive their user cost to be lower than it actually is and thus pay “too
much” to purchase a house today.
A Formula
The formula for the annual cost of homeownership, also known in the housing
literature as the “imputed rent,” is the sum of six components representing both
costs and offsetting benefits (Hendershott and Slemrod, 1983; Poterba, 1984).6 The
first component is the cost of foregone interest that the homeowner could have
earned by investing in something other than a house. This one-year cost is calculated as the price of housing P t times the risk-free interest rate r rf
t . The second
component is the one-year cost of property taxes, calculated as house price times
the property tax rate ␻ t . The third component is actually an offsetting benefit to
owning, namely, the tax deductibility of mortgage interest and property taxes for
filers who itemize on their federal income taxes.7 This can be estimated as the
6
These items should be viewed in opportunity cost terms. For example, an owner might make annual
maintenance expenditures or else allow his home to depreciate slowly in value; either way, a cost is
incurred.
7
We use the mortgage rate when computing the tax benefit of owning a house as opposed to the
Treasury rate used for the opportunity cost of capital. Mortgage rates are typically 1–2 percent above
risk-free rates of equivalent duration because borrowers typically have the options to “refinance” if
interest rates go down and to default on the mortgage if property prices fall. Homeowners can deduct
from their taxable income the additional expense associated with both of these options, but they still
Assessing High House Prices: Bubbles, Fundamentals and Misperceptions
75
effective tax rate on income times the estimated mortgage and property tax
8
payments: P t ␶ t (r m
t ⫹ ␻ t ). The fourth term reflects maintenance costs expressed as
a fraction ␦ t of home value. Finally, the fifth term, g t⫹1 , is the expected capital gain
(or loss) during the year, and the sixth term, P t ␥ t , represents an additional risk
premium to compensate homeowners for the higher risk of owning versus renting.
The sum of these six components gives the total annual cost of homeownership:
Annual Cost of Ownership ⫽ Pt rrft ⫹ Pt ␻t ⫺ Pt ␶t 共rmt ⫹ ␻t 兲 ⫹ Pt ␦t ⫺ Pt gt⫹1 ⫹ Pt ␥t .
Equilibrium in the housing market implies that the expected annual cost of
owning a house should not exceed the annual cost of renting. If annual ownership
costs rise without a commensurate increase in rents, house prices must fall to
convince potential homebuyers to buy instead of renting. The converse happens if
annual ownership costs fall. This naturally correcting process implies a “no arbitrage” condition that states that the one-year rent must equal the sum of the annual
costs of owning.9 Using the above equation, we can summarize this logic by
equating annual rent with the annual cost of ownership. We can rearrange the
annual cost of ownership by moving the price term in front of everything else on
the right-hand side to get
Rt ⫽ Pt ut ,
where the fraction u t is known as the user cost of housing, defined as
u t ⫽ r rft ⫹ ␻ t ⫺ ␶ t 共r mt ⫹ ␻ t 兲 ⫹ ␦ t ⫺ g t⫹1 ⫹ ␥ t .
The user cost u t is just a restatement of the annual total cost of ownership defined
above, but expressed in terms of the cost per dollar of house value. Expressing the
user cost in this way is particularly useful because rearranging the equation R t ⫽
P t u t as P t /R t ⫽ 1/u t allows us to see that the equilibrium price-to-rent ratio should
equal the inverse of the user cost. Thus, fluctuations in user costs (caused, for
receive their financial benefits. Thus, the U.S. government subsidizes the purchase of mortgages with
prepayment and default options.
8
While it is widely recognized that mortgage payments are tax deductible, the equity-financed portion
of a house is usually tax-subsidized as well. Owners do not pay income taxes on imputed rent (the money
they “pay themselves” as owners of a property) or capital gains taxes for all but the largest gains. Under
current tax law, gains from the sale of owner-occupied property (first and second homes) are free of
taxation as long as the gain does not exceed $250,000 for an individual or $500,000 for a married couple
and the owner has lived in the house two of the last five years. For a deeper analysis of the tax subsidy
to owner-occupied housing, see Hendershott and Slemrod (1983) and Gyourko and Sinai (2003).
9
Poterba (1984) writes the formula for the imputed rental value of housing as
R it ⫽ P it ⫺
1 ⫺ ␦ it
E 关P 兴 ⫹ 共1 ⫺ ␶ it 兲 ␻ it P it ⫺ ␶ it r t P it .
1 ⫹ r t ⫹ ␥ it it it⫹1
The rental formula in the text is an approximation of this formula.
76
Journal of Economic Perspectives
example, by changes in interest rates and taxes) lead to predictable changes in the
price-to-rent ratio that reflect fundamentals, not bubbles. Comparing price-to-rent
ratios over time without considering changes in user costs is obviously misleading.
An Illustration
For the purpose of illustrating how the user cost model works, suppose the
following: i) the risk-free 10-year interest rate r rf is 4.5 percent; ii) the mortgage rate
r m is 5.5 percent; iii) the annual depreciation rate is ␦ ⫽ 2.5 percent (Harding,
Rosenthal and Sirmans, 2004); iv) the marginal tax rate of the typical homebuyer
is ␶ ⫽ 25 percent; v) the property tax rate is ␻ ⫽ 1.5 percent; vi) the risk premium
is ␥ ⫽ 2.0 percent;10 and vii) the long-run appreciation rate of housing prices is
3.8 percent (expected inflation of 2.0 percent plus a real expected appreciation
rate of housing of 1.8 percent, the average from 1980 –2004 for the metro areas in
our sample for this paper).
Under these assumptions, the predicted user cost is 5.0 percent: that is, for
every dollar of price, the owner pays 5 cents per year in cost. Leaving aside other
differences between renting and owning, people should be willing to pay up to
20 times (1/0.05) the market rent to purchase a house.11 Hence, for example, a
two-bedroom apartment that rents for $1,000/month ($12,000/year) should sell
for up to $240,000. This price-to-rent ratio provides a baseline against which
housing prices can be judged “too high” or “too low.” If price multiplied by the user
cost exceeds the market rent, housing is relatively costly.
House Prices are More Sensitive to Changes in Real Interest Rates When Rates
are Already Low
The real interest rate is a key determinant of the user cost of housing. (Below
we explain why real long-term rather than short-term interest rates are especially
important.) A lower real interest rate reduces the user cost because the cost of debt
financing is lower, as is the opportunity cost of investing equity in a house. In
practical terms, when the real interest rate is low, homeownership is relatively
attractive because mortgage payments are low and alternative investments do not
yield much. Given that mortgage interest is tax deductible and the opportunity cost
of the equity in the house is a taxable return, a percentage point decline in the real
interest rate reduces the user cost by 1 ⫺ ␶. In our example, dropping the 10-year
rate and mortgage rates from 4.5 and 5.5 percent to 4 and 5 percent, respectively,
would cause the user cost to drop from 5 to 4.6 percent and cause the maximum
price-to-rent multiple to rise from 20 to 21.9.
Similarly, raising the income tax rate lowers the user cost of housing (Poterba,
10
We obtain this estimated risk premium from Flavin and Yamashita (2002). This risk premium may be
too high because it ignores important factors such as the insurance value of owning a house in hedging
risk associated with future changes in rents (Sinai and Souleles, 2005). However, choosing alternative
values has little effect on the time series behavior of user costs, which is the focus of this paper. A more
general model than ours would allow the relative risk of owning versus renting to vary over time.
11
They may not have to pay that amount. If housing is elastically supplied and price is above the cost
of construction, builders will create more housing at a lower multiple to rents.
Charles Himmelberg, Christopher Mayer and Todd Sinai
77
1990), making housing less expensive than renting. In the above example, changing the assumed income tax rate from 25 percent to 35 percent in the base case
example raises the sustainable price-to-rent ratio from 20 to 23.5.12 The reason is
that higher income taxes make the tax subsidy to owner-occupied housing worth
more, which lowers the cost of housing relative to other goods.
It is apparent from these calculations that the lower the user cost, the higher
the sensitivity of the rent multiple to changes in interest rates or the tax subsidy. For
example, suppose real interest rates fall by one percentage point, or 0.75 percent
after taxes. In a typical metropolitan area today with a 5 percent user cost, the user
cost falls to 4.25 and the price-to-rent ratio could rise from 20 to 23.8, an increase
of 19 percent. If the user cost were 7 percent, as it was at times during the early
1980s, the same one percentage point decline in real interest rates would cause a
smaller 12 percent rise in the justifiable price-to-rent ratio. Thus, in the current low
real interest rate environment, a given decrease in real rates induces a larger
potential percentage increase in house prices than the same decrease in real rates
would cause starting from a high interest rate. Of course, the reverse is true, too: an
unexpected rise in long-term real interest rates from their current low base would
cause a disproportionately large percentage decline in the price people would be
willing to pay, assuming rents stay constant.
House Prices are More Sensitive to Changes in Real Interest Rates in High
Appreciation Rate Cities
We have thus far downplayed one of the most critical and least understood
determinants of the user cost of housing—the expected growth rate of housing
prices. Expected price appreciation is central to the debate over whether a housing
bubble exists and, if so, where.
Evidence suggests that expected rates of house price appreciation may differ
across markets. Because expected appreciation is subtracted from the user cost,
metropolitan areas where expected house price appreciation is high have lower
user costs than areas where expected house price appreciation is low. Any given
change in real interest rates, then, operates on a lower user cost base in high price
growth cities, yielding a larger percentage effect. For example, if in the above
example we had assumed that the expected real rate of appreciation on housing
was 2.8 percent rather than 1.8 percent, the predicted user cost would have been
4 percent instead of 5, and the potential price-to-rent ratio would have been 25
instead of 20. If we had assumed an even higher rate of expected price growth, say
3.8 percent, the predicted user cost would have been 3 percent and the implied
price-to-rent ratio would have been 33.3. (Lest this seem incredible, that is about
equal to the price-to-rent ratio in the San Francisco metropolitan area, calculated
as the ratio of the mean house value divided by the mean rent in the 2000 Census.)
12
Of course, this calculation does not account for the fact that higher taxes would presumably cause
rents to fall, the net effect of which may or may not cause housing prices to fall. As Poterba (1990)
explains, whether this happens or not depends on the extent to which the increased tax differential
between and housing and nonhousing causes consumers to choose more housing.
78
Journal of Economic Perspectives
Thus, a 1 percentage point decline in real interest rates could raise house prices by
as much as 19 percent in a location that averaged 1.8 percent price growth location
and 33 percent in a 3.8 percent price growth market.
A large degree of variation across cities in expected growth rates is plausible,
given what we know about land price dynamics in cities. Of course, if the long-run
supply of housing were perfectly elastic, house prices would be determined solely by
construction costs, and expected appreciation would be the expected growth rate
in real construction costs (Muth, 1960). At the national level, real construction
costs have fallen over the past 25 years, yet over the same time period, real
constant-quality house prices have grown. When we looked at construction costs in
different metropolitan areas using data from R.S. Means Company,13 we found that
house prices grew relative to construction costs in most of the metropolitan
statistical areas in our analysis. Changes in construction costs explain neither the
overall rise in real house prices nor cross-sectional differences in appreciation rates
across markets.
The long-run growth of house prices in excess of construction costs suggests
that the underlying land is appreciating faster than the structures. This finding is
consistent with classic theories of urban development in which the growth of cities
is accompanied by (or driven by) benefits of increasing density and agglomeration.
Since the supply of land near urban centers (either a city center or suburban
subcenters) is in short supply, the demand for housing generated by such economic
growth is capitalized into land prices.14 Indeed, some metropolitan areas have
persistently high rates of house price appreciation over very long periods of time.
Gyourko, Mayer and Sinai (2004) refer to cities with high long-run rates of house
price growth as “superstar cities.” They argue that because of tight supply constraints combined with an increasing number of households who want to live in the
area, a city can experience above-average house price growth over a very long
horizon. They present evidence from the U.S. Census since 1940 showing that real
house price appreciation in superstar cities such as San Francisco, Boston, New
York and Los Angeles has exceeded the national average by one to three percentage points per year over a 60-year period. In addition, the average growth rate of
housing prices over the 30-year period 1940 –1970 has a correlation of 0.40 with the
subsequent 30-year average over 1970 –2000. This fact suggests that differences in
appreciation rates of housing across metropolitan statistical areas are persistent
over long periods and reflect more than just secular changes in industrial concentration (like the high technology boom) or household preferences.
A related finding is that price-to-rent differences across cities are persistent
over time: cities with high price-to-rent ratios tend to remain high, and those with
low price-to-rent ratios remain low. This fact is predicted by the user cost theory if
purchasers in these “superstar” markets are correctly anticipating sustained future
13
See Glaeser and Gyourko (2004) for more information on RS Means data and a detailed discussion
of the issues involved in measuring construction costs across cities.
14
See the Spring 1998 “Symposium on Urban Agglomeration” in this journal for more detail on these
arguments, especially the papers by Edward Glaeser (1998) and John Quigley (1998).
Assessing High House Prices: Bubbles, Fundamentals and Misperceptions
79
appreciation, because buyers in superstar cities should be willing to pay more for a
house if they expect rents to rise in the future. Indeed, Sinai and Souleles (2005)
find statistical evidence using data from 44 metropolitan areas that the cities with
the highest price-to-rent ratios also have the highest expected growth rates of prices
and rents.15
Calculating the User Cost
To examine how these cost factors are related to house price changes, we
compute the user cost of housing for each of the 46 metro areas in our sample. As
is often true with theoretical constructs, solving for the user cost in practice poses
a number of difficult challenges.
First, theory suggests that we measure the risk-free interest rate using a
representative rate like the yield on a one-year U.S. Treasury bill. In practice,
however, it is important to consider simultaneously the impact of expected
future real interest rates on the expected appreciation rate of future house
prices (the fifth term in our user cost equation). For example, in 2004, real
short-term interest rates were well below real long-term rates, suggesting that
the bond market anticipated that real short-term interest rates would rise in the
future. When short-term rates are expected to rise, potential homeowners
should also anticipate (assuming that land will be inelastically supplied in the
market) that the annual cost of ownership will also rise, implying that future
house prices should fall (or rise less than they otherwise would). Thus, a higher
real interest rate “spread”—the long-term minus short-term rate—suggests a
relatively lower expected growth rate of future house prices. This predictable
decline in the future growth rate of house prices should roughly equal the
spread. Hence, if we plug the spread into our user cost formula in place of gt⫹1,
the short-term rate drops out, and all that remains is the long-term rate. In sum,
when a constant rate of future price appreciation is assumed for the user cost
formula, it is probably more sensible to measure the opportunity cost of funds
using a real long-term interest rate. This subtle point is often ignored in
empirical research. In our calculations below, we use the constant yield to
maturity on 10-year Treasuries and convert this to a real rate by subtracting the
10-year expected inflation rate from the Livingston Survey. If we were to
substitute the one-year Treasury rate into our user cost calculations instead of
the 10-year rate, it would make housing in 2004 look even less costly in every
market in our sample.
15
We have found a similar persistence of price-to-rent ratios across markets using data from the 1980
and 2000 Integrated Public Use Microsample from the U.S. Decennial Census to compute the price/
income ratio at the household level for homeowners and the rent/income ratio at the household level
for renters. We then took the average of each ratio by metropolitan statistical area and decade.
Price-to-rent at the metropolitan area-decade level is then calculated as MEAN(price/income)/MEAN
(rent/income).
80
Journal of Economic Perspectives
A second, closely related challenge is that we cannot observe households’
expected growth rate of housing prices. By using long-term instead of shortterm real interest rates in the user cost, we already account for predictable
changes in house prices arising from predictable changes in short-term interest
rates. But house prices also rise in response to higher rents. We assume that user
costs do not change over long horizons and that hence rents at the level of a
metropolitan area grow at the same rate as real housing prices in that metro
area. We therefore measure expected future rent growth using the average real
growth rate of house prices from 1940 –2000 from Gyourko, Mayer and Sinai
(2004).
Finally, it is important to recognize that metro areas also differ in their typical
federal income taxes and local property tax rates. Cities with higher per capita
income have higher effective marginal income tax rates, which lead to higher
price-to-rent ratios due to the greater value of the tax subsidy to owner-occupied
housing. We use average property tax rates from Emrath (2002) and income tax
rates which we collect from the TAXSIM model of the National Bureau of Economic Research.16 However, data from the Internal Revenue Service show that
65 percent of tax-filing households do not itemize their tax deductions and, if they
are homeowners, do not benefit from the tax deductibility of mortgage interest and
property taxes.17 To account at least roughly for the higher cost of owning for the
nonitemizers, we reduce the tax subsidy in our calculations by 50 percent.
Table 2 shows how user cost can vary across cities and within cities over time.
The average user costs in the highest growth rate markets are less than half as big
as they are in the highest user cost markets—for example, 3.3 percent in San Jose
versus 7.1 percent in Pittsburgh. This range of user costs implies average potential
price-to-rent ratios ranging from 33 to 14, respectively. By 2004, user costs had
fallen significantly below the long-run average—2.0 percent in San Jose versus
5.7 percent in Pittsburgh. That is, the price-to-rent ratio could have risen to 50 in
San Jose but just 18 in Pittsburgh. To illustrate how much a low initial user cost
matters for price swings, San Francisco experienced a user cost decline from an
average of 3.7 percent to 2.4 percent in 2004, implying a multiple expansion from
27 to 42. In some cities, user cost has declined more than 40 percent since the
previous house price peak, while in other cities the decline has been as low as
10 percent. Since the user cost is just the inverse of the price-to-rent ratio, these
16
While the net benefits of services financed by local property taxes presumably benefit owners and
renters equally, a higher property tax nevertheless lowers the price-to-rent ratio because the tax is
implicitly included in rents but not home prices.
17
Sources: IRS Statistics of Income, Table 1—Individual Income Tax, All Returns: Sources of Income
and Adjustments, and Table 3—Individual Income Tax Returns with Itemized Deductions, for 2002.
Available at 具http://www.irs.gov/pub/irs-soi/02in01ar.xls典 and 具http://www.irs.gov/pub/irs-soi/
02in03ga.xls典. Even without itemizing, all homeowners benefit from some tax subsidy. If a homeowner
were to rent his property out, he would have to report the rent received as taxable income. A
homeowner does not need to report the “imputed rent” he pays himself as taxable income and thus
saves the income tax he would have otherwise paid the government. Gyourko and Sinai (2003) show that
the mortgage interest and property tax deduction components comprise about one-third of the total
subsidy.
Charles Himmelberg, Christopher Mayer and Todd Sinai
81
Table 2
How User Cost Varies Across Cities and Over Time
Average
user cost
User cost
in 2004
% change in
user cost since
prior peak
Markets where house prices peaked in the late 1980s and had a trough in the 1990s:
Atlanta, GA
5.3%
3.9%
⫺31%
Austin, TX
6.0%
4.5%
⫺42%
Baltimore, MD
5.7%
4.3%
⫺29%
Boston, MA
5.3%
4.0%
⫺34%
Dallas, TX
6.4%
4.9%
⫺17%
District of Columbia, DC
5.6%
4.4%
⫺28%
Jacksonville, FL
4.9%
3.4%
⫺23%
Los Angeles, CA
4.4%
3.1%
⫺38%
Nashville, TX
5.5%
4.0%
⫺31%
New York, NY
6.0%
4.8%
⫺29%
Norfolk, VA
5.6%
4.2%
⫺33%
Oakland, CA
4.2%
2.9%
⫺39%
Orange County, CA
3.7%
2.5%
⫺41%
Philadelphia, PA
6.6%
5.2%
⫺27%
Phoenix, AZ
4.7%
3.3%
⫺23%
Portland, OR
6.0%
4.7%
⫺11%
Raleigh-Durham, NC
5.2%
3.8%
⫺19%
Richmond, VA
6.1%
4.7%
⫺27%
Sacramento, CA
4.7%
3.5%
⫺28%
San Bernadino-Riverside, CA
4.6%
3.3%
⫺36%
San Diego, CA
4.1%
2.9%
⫺40%
San Francisco, CA
3.7%
2.4%
⫺41%
San Jose, CA
3.3%
2.0%
⫺46%
Seattle, WA
4.9%
3.4%
⫺38%
Markets where house prices were high in the early 1980s and rebounded in the 2000s:
Charlotte, NC
5.2%
3.8%
⫺35%
Chicago, IL
6.3%
4.9%
⫺30%
Cincinnati, OH
6.5%
5.1%
⫺14%
Cleveland, OH
6.4%
5.0%
⫺14%
Columbus, OH
6.2%
4.8%
⫺15%
Denver, CO
5.1%
3.7%
⫺42%
Detroit, MI
6.6%
5.2%
⫺11%
Fort Lauderdale, FL
5.8%
4.3%
⫺42%
Indianapolis, IN
6.0%
4.5%
⫺16%
Kansas City, KS
5.7%
4.2%
⫺16%
Memphis, TN
6.0%
4.5%
⫺29%
Miami, FL
6.2%
4.8%
⫺15%
Milwaukee, MN
7.0%
5.7%
⫺5%
Minneapolis, MN
5.6%
4.3%
⫺10%
Orlando, FL
5.9%
4.4%
⫺42%
Pittsburgh, PA
7.1%
5.7%
⫺12%
St. Louis, MO
6.1%
4.7%
⫺15%
Tampa, FL
6.1%
4.6%
⫺18%
Markets where house prices have declined since the early 1980s and never fully rebounded:
Fort Worth, TX
6.2%
4.7%
⫺15%
Houston, TX
6.7%
5.2%
⫺38%
New Orleans, LA
5.3%
3.9%
⫺17%
San Antonio, TX
6.9%
5.4%
⫺42%
% change in
user cost since
prior trough
⫺26%
⫺22%
⫺22%
⫺21%
⫺18%
⫺22%
⫺25%
⫺27%
⫺21%
⫺20%
⫺23%
⫺30%
⫺33%
⫺19%
⫺6%
⫺20%
⫺20%
⫺21%
⫺25%
⫺26%
⫺30%
⫺34%
⫺33%
⫺25%
⫺6%
⫺24%
⫺22%
⫺36%
⫺23%
⫺28%
⫺41%
⫺23%
⫺25%
⫺7%
⫺23%
⫺21%
⫺33%
⫺18%
⫺23%
⫺18%
⫺7%
⫺22%
⫺19%
⫺20%
⫺28%
⫺23%
82
Journal of Economic Perspectives
examples demonstrate how heterogeneous changes in user cost can help explain
the heterogeneity of price and price-to-rent growth across cities. More formally, the
cross-sectional correlation between the percentage change in user costs (the second column of Table 2) and the percentage change in price-to-rent (the third
column of Table 1) between 1995 and 2004 is ⫺0.6.
Finally, it is worth noting that these computations do not account for all factors
that could affect the spread in user costs between high and low appreciation rate
cities. In high-priced cities, the value of structures is generally small relative to the
value of the land on which they sit, which suggests that physical depreciation is
small as a fraction of total property value. Lower depreciation rates (relative to
value) in high land cost markets such as San Francisco and New York would lower
their user costs and further increase their price-to-rent ratios relative to other cities.
Our calculations do not allow for this.
At the same time, lower depreciation rates in cities like San Francisco might be
offset by higher house price risk. Some research has argued that housing in
high-priced cities is riskier because the standard deviation of house prices is much
higher (Case and Shiller, 2004; Hwang and Quigley, 2004), while other research
argues that homeowners can partially hedge this rent and price risk (Sinai and
Souleles, 2005).18 Since this hedge is imperfect, however, we would still expect risk
premiums would be somewhat higher in the highest price-to-rent markets, narrowing the predicted cross-sectional difference in user costs between cities like San
Francisco and Milwaukee, say. Our calculations do not allow for this effect, either.
Are Current House Prices Too High?
One way to assess whether house prices are too high is to calculate the imputed
rent on housing and compare it to actual rents available in the market. The
imputed rent is the user cost times the current level of house prices obtained from
the OFHEO price index.
We create an index of the imputed-to-actual-rent ratio by dividing the imputed
rent index by the index of market rents. This index lets us assess whether the
imputed cost of owning a house relative to renting the same unit has changed
within each metropolitan area over time and whether the index in 2004 is at or near
its previous peak level. We cannot make comparisons of imputed-to-actual-rent
levels across cities, nor can we explicitly calculate whether the index is “too high”
at any given point in time, but we can come close by comparing the index to its
25-year average.
We set the within-city 25-year average of the index equal to 1.0 in each city.
Figure 2 plots the imputed-to-actual-rent index for 12 representative cities. We also
include the equivalent price-to-rent index for these cities to highlight the times that
the price-to-rent index differs from the imputed-to-actual-rent ratio. In Figure 2,
18
Davidoff (2005) shows that the demand for owned housing decreases as the covariance between labor
income and house prices rises. By that logic, the price-to-rent ratio also should be lower in markets
where the typical homebuyer’s wage income is closely tied to the local economy—in one-company towns,
for instance, or cities with a high concentration in a single industry.
Assessing High House Prices: Bubbles, Fundamentals and Misperceptions
83
Figure 2
Imputed-to-Actual-Rent Ratio versus Price-to-Rent Ratio
(ratios normalized to their 25-year average)
1980
1990
2000
1.5
.5
1
1.5
1
.5
.5
1
1.5
2
Denver
2
Chicago
2
Boston
1980
2000
2000
2
1
.5
1980
1990
2000
2000
2
New York
1
1990
2000
1980
2000
2
.5
1
1.5
2
1.5
1
2000
1990
San Francisco
.5
1
1.5
2
San Diego
.5
1990
2000
.5
1980
Portland
1980
1990
1.5
2
1.5
.5
1
1.5
1
.5
1990
1980
Minneapolis
2
Miami
1980
2000
1.5
2
1.5
.5
1990
1990
Los Angeles
1
1.5
1
.5
1980
1980
Houston
2
Detroit
1990
1980
1990
2000
1980
1990
2000
Imputed rent/Actual rent
Price/Actual rent
Source: Authors’ calculations.
Houston represents the small group of cities that have been experiencing declining
prices and imputed rent ratios over 25 years. Chicago, Detroit, Miami and Indianapolis are indicative of the middle panel cities that have U-shaped prices and
imputed rent ratios. The remaining cities are representative of the cyclical first
Table 3
User Cost-Based Assessments of House Price Levels
Imputed-to-actual-rent ratio
At
sample
peak
Markets where the imputed rent-rent
Boston, MA
District of Columbia, DC
Los Angeles, CA
New York, NY
Oakland, CA
Orange County, CA
Philadelphia, PA
Portland, OR
San Bernadino-Riverside, CA
San Diego, CA
San Francisco, CA
San Jose, CA
Markets where the imputed rent-rent
Baltimore, MD
Chicago, IL
Cincinnati, OH
Cleveland, OH
Columbus, OH
Denver, CO
Detroit, MI
Fort Lauderdale, FL
Jacksonville, FL
Kansas City, KS
Miami, FL
Milwaukee, MN
Minneapolis, MN
New Orleans, LA
Phoenix, AZ
Pittsburgh, PA
Sacramento, CA
Seattle, WA
St. Louis, MO
Tampa, FL
Markets where the imputed rent-rent
Atlanta, GA
Austin, TX
Charlotte, NC
Dallas, TX
Fort Worth, TX
Houston, TX
Indianapolis, IN
Memphis, TN
Nashville, TX
Markets where the imputed rent-rent
Norfolk, VA
Orlando, FL
Raleigh-Durham, NC
Richmond, VA
San Antonio, TX
At
sample
trough
In
2004
% of
years
below
2004
Imputed-rent-to-income ratio
At
sample
peak
At
sample
trough
In
2004
% of
years
below
2004
ratio peaked in the late 1980s and had a trough in the 1990s:
1.37
0.67
1.02
60%
1.40
0.72
1.03
60%
1.24
0.76
1.02
56%
1.32
0.76
0.99
56%
1.42
0.68
1.03
56%
1.43
0.74
1.07
60%
1.52
0.62
0.95
52%
1.43
0.69
1.07
72%
1.35
0.72
1.08
64%
1.37
0.72
0.98
48%
1.42
0.69
1.00
52%
1.39
0.72
1.05
60%
1.27
0.78
0.99
52%
1.32
0.76
0.89
32%
1.27
0.75
1.13
76%
1.26
0.77
1.00
48%
1.37
0.76
1.05
48%
1.35
0.74
1.12
68%
1.33
0.70
1.08
68%
1.35
0.73
1.10
64%
1.52
0.71
0.97
48%
1.45
0.72
0.92
44%
1.51
0.67
1.04
64%
1.46
0.70
0.84
20%
ratio was high in the early 1980s and flat or rising by the 2000s:
1.34
0.78
0.96
36%
1.36
0.73
0.89
32%
1.31
0.81
1.01
56%
1.27
0.83
0.96
48%
1.34
0.78
0.91
24%
1.40
0.71
0.77
8%
1.25
0.82
0.96
36%
1.29
0.78
0.84
8%
1.22
0.81
0.93
28%
1.43
0.71
0.77
8%
1.46
0.70
0.90
28%
1.60
0.66
0.85
24%
1.28
0.70
1.16
88%
1.31
0.76
0.95
28%
1.45
0.73
1.07
60%
1.61
0.71
1.04
64%
1.53
0.73
0.88
32%
1.68
0.67
0.80
28%
1.46
0.74
0.88
28%
1.55
0.68
0.75
16%
1.31
0.77
1.12
80%
1.52
0.74
1.12
72%
1.15
0.79
1.14
88%
1.28
0.83
0.93
32%
1.23
0.79
1.14
88%
1.45
0.73
0.97
56%
1.46
0.71
0.88
16%
1.76
0.61
0.69
12%
1.46
0.71
0.89
28%
1.66
0.66
0.78
20%
1.22
0.84
0.97
32%
1.41
0.73
0.78
8%
1.46
0.76
0.99
56%
1.39
0.73
1.09
68%
1.37
0.77
0.96
40%
1.35
0.75
0.87
20%
1.21
0.84
0.96
28%
1.46
0.71
0.80
20%
1.43
0.78
0.98
56%
1.55
0.72
0.92
48%
ratio has declined since the early 1980s and never rebounded:
1.44
0.76
0.86
24%
1.55
0.70
0.79
20%
1.55
0.72
0.79
16%
1.71
0.66
0.70
8%
1.34
0.73
0.81
12%
1.54
0.64
0.71
8%
1.50
0.67
0.74
8%
1.71
0.62
0.66
12%
1.55
0.66
0.72
8%
1.71
0.60
0.64
8%
1.76
0.68
0.74
12%
1.81
0.62
0.66
16%
1.22
0.81
0.90
20%
1.48
0.66
0.70
4%
1.37
0.70
0.76
8%
1.56
0.60
0.64
4%
1.32
0.75
0.84
12%
1.55
0.63
0.69
8%
ratio has declined since the early 1980s and never rebounded: (continued)
1.49
0.73
0.88
20%
1.49
0.69
0.86
24%
1.50
0.75
0.88
36%
1.58
0.72
0.84
36%
1.26
0.72
0.80
12%
1.56
0.65
0.72
12%
1.40
0.78
0.90
24%
1.44
0.72
0.84
20%
1.61
0.67
0.74
12%
1.83
0.59
0.62
8%
Notes: Twenty-five year within-MSA average is normalized to 1.00. Values are not comparable across
markets.
Charles Himmelberg, Christopher Mayer and Todd Sinai
85
Figure 3
Real 10-Year Interest Rates
10
Interest rate
7.5
5
2.5
0
1980
1985
1990
1995
2000
2005
Source: Federal Reserve Bank H.15 Release, Federal Reserve Bank Livingston Survey: 10-year expected
inflation.
panel and include some of the highest profile markets on the east and west coasts.
Table 3 reports the value of the imputed-to-actual-rent index for all 46 cities at
some key dates.
We highlight two important results. First, the imputed-to-actual-rent ratio does
not suggest widespread or historically large mispricing of owner-occupied properties in 2004. For all three groups of cities, the imputed rent associated with buying
a house in 2004 is not nearly as high relative to actual rents as it was in the past.
Only seven cities have an imputed-to-actual-rent ratio that is within 20 percent of its
previous peak and, of those, Detroit, Milwaukee and Minneapolis are the closest. By
contrast, 12 cities have imputed-to-actual-rent ratios 40 percent or more below their
historical peak levels. In fact, the 2004 levels of imputed-to-actual-rent are hardly
atypical. In Portland, Oregon, the 2004 imputed-to-actual-rent ratio exceeds the
value of the ratio in prior years about 75 percent of the time (88 percent in
Detroit). But in high-price growth cities like Orange County and San Francisco, the
imputed-to-actual-rent ratio in the previous 24 years was higher than its 2004 value
about half the time. While owner-occupied housing is not nearly as expensive
relative to renting as it has been at times over the past 24 years, housing in a few
markets appears somewhat expensive relative to the recent past.
A second key observation is that deviations between the imputed rent and
actual rent appear strongest when real interest rates were unusually high (early
1980s) or unusually low (2001–2004). A comparison of Figures 2 and 3 makes this
point quite clear. Thus, the recent run-up in house prices appears to be primarily
driven by fundamental economic changes. Of course, in Boston, New York, Los
Angeles, San Diego and San Francisco in the late 1980s and Denver, Miami and
86
Journal of Economic Perspectives
Houston in the mid-1980s, a high imputed-to-actual-rent ratio was a prelude to
sizable housing downturns. Hence, our methodology successfully identifies prior
periods of excessive valuations in the housing market.
The imputed rent-to-income ratio provides an alternative measure of housing
valuations. While the imputed-to-actual-rent ratio would be high if there were a housing
bubble, house prices could still fall if current housing costs were unsustainable given
households’ abilities to pay. The ratio of imputed rent to income provides a better
indicator of whether house prices are supported by underlying demand. In particular,
rising housing prices or rising user costs need not imply that households are being
priced out of the market if incomes are rising, too. In a bubble market, by contrast, we
would expect to see the annual cost of homeownership rising faster than incomes, thus
raising imputed rent-to-income to unsustainable levels.
Figure 4 reports the ratio of the imputed rent of owner-occupied housing to
income for 12 cities, with a matching panel in Table 3.19 For comparison, Figure 4
also shows the more commonly used metric of house price-to-income. These ratios
were calculated in the same way as the imputed-to-actual-rent ratio, except that
we now divide imputed rent by an index of income per capita at the level of the
metropolitan statistical area constructed from BEA data. We set the index value
of 1.0 to correspond to the 25-year average for each metropolitan area of each
ratio.
These calculations lead us to similar conclusions as in the previous section.
None of the metropolitan areas that we have featured appears to be at a peak level
of costliness in 2004 (relative to the past 24 years). In fact, only nine of our 46 cities
have housing costs above their average historical levels relative to per capita
income. Even so, the range across cities in the 2004 imputed rent-to-income
measure, which varies from 1.12 in Miami to 0.62 in San Antonio, is much tighter
than the within-city variation over time. Indeed, in Miami, the imputed rent-toincome ratio has a historical peak-trough range of more than 50 percent. One
might object to these historical comparisons on the grounds that prices during the
1980s were unusually high. If we remove the 1980s data, it is still the case that only
southern California and south Florida look relatively expensive.
Outliers for the ratios of imputed-rent-to-income or price-to-income are most
pronounced in years when real interest rates are historically high or historically low.
Just as with our imputed-to-actual-rent ratio, a high imputed-rent-to-income ratio
has been a prelude to subsequent price declines. Despite having been corrected to
recognize differences in user costs, the imputed rent-to-income ratio comes with an
important caveat. Households at the median income may be poorer than the
marginal buyers of median-priced homes. For example, Gyourko, Mayer and Sinai
(2004) argue that the marginal homebuyers in “superstar” cities are high-income
households who have moved from other parts of the country. This pattern would
imply that the median homes in such cities are purchased by new residents whose
In an appendix appended to the on-line version of this paper at 具http://www.e-jep.org典, Figure 2 shows our
calculated imputed-to-actual-rent ratios for another 33 metropolitan statistical areas in our data. Also in the
appendix, Figure 3 shows our calculated imputed-to-actual-rent ratios for another 33 metropolitan areas.
19
Assessing High House Prices: Bubbles, Fundamentals and Misperceptions
87
Figure 4
Imputed-Rent-to-Income Ratio versus Price-to-Income Ratio
(ratios normalized to their 24-year average)
Denver
1.5
1
1.5
1
1980
1990
2000
.5
.5
.5
1
1.5
2
2
Chicago
2
Boston
1980
2000
2000
2
1
.5
1980
1990
2000
1.5
1
.5
1980
1990
2000
2000
1.5
2
2
.5
1
1
.5
2000
1990
San Francisco
1.5
1.5
1
.5
1990
1980
San Diego
2
Portland
1980
2000
2
2
1.5
.5
2000
1990
New York
1
1.5
1
.5
1990
1980
Minneapolis
2
Miami
1980
2000
1.5
2
1
.5
1990
1990
Los Angeles
1.5
1.5
1
.5
1980
1980
Houston
2
Detroit
1990
1980
1990
2000
1980
1990
2000
Imputed rent/Income
Price/Income
Source: Authors’ calculations.
income exceeds that of the median income. Also, Ortalo-Magnè and Rady (2005)
argue that homeowners whose incomes do not grow as fast as house prices in an
area can remain homeowners since their housing wealth rises commensurately with
prices. Thus, they can appear to be low income, but that is because the implicit
88
Journal of Economic Perspectives
income from their housing wealth is not reflected in the denominator of the
imputed rent-to-income ratio. For these reasons, our measure of the imputed
rent-to-income ratio in high price growth markets is likely to be higher than the
true underlying concept. Ideally, we would also want to consider wealth ratios when
assessing the extent of housing market excess.
But even given this caveat, housing prices at the end of 2004 did not look
particularly out of line with past patterns of rents or incomes. This conclusion holds
true even in cities like Boston, New York and San Francisco, where housing prices
were high and rose even higher from 2000 to 2004. Only a handful of cities—
namely Miami, Fort Lauderdale, Portland and San Diego— had imputed-to-actualrent and imputed rent-to-income ratios that both were higher relative to the recent
past, but even they had not yet risen to approach previous historical peak levels.
What Might Be Missing in these Calculations?
One obviously important factor over the past 25 years that we have omitted
from our analysis is cost-reducing innovations in the mortgage market. Data from
the Federal Housing Finance Board suggest that in 1980, initial fees and “points” (a
point is an up-front fee equal to 1 percent of the loan amount) were typically about
2 percent of the value of a loan; by 2004, they were less than one-half of 1 percent.
Lower origination costs may be a factor in the greater willingness of homeowners
to refinance their mortgage in response to decreases in interest rates (Bennett,
Peach and Peristiani, 2001). Since lower origination costs are likely a permanent
change in the mortgage market, demand for housing may be permanently higher,
lowering the imputed rent associated with owning a house in the latter portion of
our sample period.
An alternative hypothesis sometimes advanced for the recent rapid growth in
housing prices is that it has become easier to borrow, so that overall demand for
homeowning has risen. Certainly, average mortgage amounts have risen much
faster than inflation or incomes, growing by over $120,000 since 1995 to a record
high of over $261,000 in 2003. Yet average down payments amounts have grown
even faster. The average new first mortgage in 2003 had a down payment that
exceeded 25 percent of the house value, nearly five percentage points higher than
in 1995. Lest one fear that these aggregate statistics mask a number of liquidityconstrained households, the percentage of household with a loan-to-value ratio at
or above 90 percent fell from 25 percent to 20 percent of all borrowers between
1997 and 2003. In addition, down payment percentages are the highest (and thus
loan-to-value ratios are lowest) in the most expensive cities. Down payments for
buyers in San Francisco and New York averaged 39 and 34 percent of their house
value, respectively. We suspect that this occurs in part because existing homeowners
use large capital gains to put more money down on their next house. One caveat:
if homeowners are extracting equity using second mortgages, and doing so disproportionately in the most expensive cities, our data would underestimate their true
leverage. However, it would take considerable borrowing through that channel to
offset the increase in down payments we observe.
A related concern is that if many people have borrowed using adjustable rate
Charles Himmelberg, Christopher Mayer and Todd Sinai
89
mortgages, they may be especially vulnerable to an in increase in interest rates.
From 2001–2003, adjustable rate mortgages made up fewer than 20 percent of all
new mortgages, a rate that is lower than all but one year in the 1990s. However, the
use of adjustable rate mortgages did rise to 34 percent of new mortgages in 2004.
While buyers in high-priced cities are more likely than average to take out adjustable rate mortgages, the use of adjustable rate mortgages also fell disproportionately in the most expensive cities, with declines from 1995–2003 of 21 and 16 percent in San Francisco and New York, respectively (the decline in Boston was smaller).
Even so, if any of the above considerations were actually spurring spending in
the housing market, our analysis should pick it up as more costly homeownership.
Demand driven by looser restrictions on obtaining credit, for example, should lead
to higher house prices. In our analysis, the higher price would raise the imputed
rent, and the imputed-to-actual-rent and imputed rent-to-income ratios would rise.
We do not observe this, at least by the end of 2004. The last time such factors
(anecdotally, at least) affected the housing market was in the late 1980s, and that
mispricing is very apparent in our data.
Yet another potential shortcoming of our analysis is that we assume low-cost
arbitrage between owning and renting. In reality, mortgage origination fees, broker
commissions and moving costs make it expensive to switch back and forth between
owning and renting. These transaction costs imply a range within which imputed
rents may deviate from actual rents before market forces work to close the gap.
Arbitrage arguments may also fail because the characteristics of rental units and
owned homes may differ substantially, in which case imputed rent comparisons are
less meaningful.
Finally, our valuation ratios may be biased due to trends in unmeasured quality
differences between owned and rented units. We have no reason to believe that the
quality of owner-occupied housing has systematically declined relative to that of
rental housing. If anything, the reverse is likely true due to the strong growth in
home renovation expenditures. If the quality of existing single-family homes is
rising, the OFHEO price index might overstate housing appreciation rates for a
constant quality house.
Conclusion
We have discussed how to calculate the local annual cost of owner-occupied
housing and how to construct measures of home values by comparing this cost to
local incomes and rents. Doing so reveals past periods like the late 1980s when the
cost of owning looked quite high relative to incomes or the cost of renting. In 2004,
however, these same measures show little evidence of housing bubbles in almost
any of the markets we have studied. Constant-quality data on house prices and rents
exist for less than three decades, cover only two house price booms and are not
comparable across different cities. Hence, it is impossible to state definitively
whether or not a housing bubble exists. However, we can say that most housing
markets did not look much more expensive in 2004 than they looked over the past
90
Journal of Economic Perspectives
10 years, and in most major cities our valuation measures are nowhere near their
historic highs.
We hope that three main insights emerge from our analysis. First, house price
dynamics are a local phenomenon, and national-level data obscure important
economic differences among cities. Moreover, one cannot draw conclusions about
house prices by comparing cities: price-to-income and price-to-rent ratios that
would be considered “high” for one city may be typical for another. Second, when
considering local house prices, the economically relevant basis for comparison is
the annual cost of ownership. Without accounting for changes in real long-term
interest rates, expected inflation, expected house price appreciation and taxes, one
cannot accurately assess whether houses are reasonably priced. Third, changes in
underlying fundamentals can affect cities differently. In particular, in cities where
housing supply is relatively inelastic, prices will be higher relative to rents, and
house prices will typically be more sensitive to changes in interest rates.
Our evidence does not suggest that house prices cannot fall in the future if
fundamental factors change. An unexpected rise in real interest rates that raises
housing costs, or a negative shock to a local economy, would lower housing
demand, slowing the growth of house prices and possibly even leading to a house
price decline. However, this fact does not mean that today houses are systematically
mispriced.
y The authors would like especially to thank Steven Kleiman and Reed Walker for extraordinary research support and Joseph Gyourko, James Hines, Steven Kleiman, Jonathan
McCarthy, Richard Peach, Allen Sinai, Timothy Taylor, Michael Waldman, Neng Wang and
seminar participants at Columbia Business School for many helpful comments. The Paul
Milstein Center for Real Estate at Columbia Business School and the Zell/Lurie Real Estate
Center at Wharton provided funding. The views expressed in the paper are solely those of the
authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or
the Federal Reserve System.
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